A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by : 1. Graph (1): B vs r, curve rising from origin, concave up, increasing steeply 2. Graph (2): B vs r, straight line from origin 3. Graph (3): B vs r, linear rise to a peak then decreasing 4. Graph (4): B vs r, curve rising steeply then flattening

Answer: 3. Graph (3): B vs r, linear rise to a peak then decreasing Key idea: use Ampere's law inside and outside the cable. Inside ( r Outside ( r>R ): B=μ₀I/2π r∝1/r : it decreases. The maximum is at r=R , so the graph rises linearly and then falls as 1/r : graph (3).

Topic: Ampere's law: straight wire and solenoid· Magnetic Effects of Current and Magnetism

A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by :

A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by :

four B versus r graphs, options (1) to (4)

1. Graph (1): B vs r, curve rising from origin, concave up, increasing steeply

2. Graph (2): B vs r, straight line from origin

3. Graph (3): B vs r, linear rise to a peak then decreasing

4. Graph (4): B vs r, curve rising steeply then flattening

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Answer: 3. Graph (3): B vs r, linear rise to a peak then decreasing

Key idea: use Ampere's law inside and outside the cable.

Inside (\(r
Outside (\(r>R\)): \(B=\dfrac{\mu_0I}{2\pi r}\propto\dfrac1r\): it decreases.

The maximum is at \(r=R\), so the graph rises linearly and then falls as \(1/r\): graph (3).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by :

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